Australia's freshly elected federal opposition leader, Bill Shorten has left the door open to bringing in a private member's bill to allow same-sex marriage when parliament sits.

Malcolm Turnbull has promised to legislate for a plebiscite to be held on the issue by the end of the year, but Labor says it's a waste of $160 million.

'I get to choose the words I use': Liberals dodge gay marriage vote questionsSenior Liberals Scott Morrison and Julie Bishop have repeatedly refused to answer questions about how they would vote on same-sex marriage legislation.

"Let's see what we do when we get back to parliament, but I remain completely committed to the view that the quickest and easiest way to deal with the debate on marriage equality is have a parliamentary vote," Mr Shorten told reporters in Melbourne on Monday.

Mr Turnbull, who is in favour of the law change, believes a successful national vote would ensure same-sex marriage laws sailed through parliament.

"I think Mr Turnbull needs to pick up one of the lessons from this election ... the more you stick to your own conscience and what you believe, the better this country will run."

Mr Shorten reiterated Labor's position that a national debate would bring out "destructive, homophobic arguments".

Some newly elected gay conservative candidates are still backing a plebiscite thinking that it will enable the people to "have their say" - however what they continue to forget is that the Howard Government did not ask the people when not amended the Marriage Act in the first place to exclude LGBTQIA couples in the first place.

Relationship recognition for gay couples in NSW moved one step forward tonight after the government passed the relationship register in the lower house with the bill passing 62 votes to 9. After just three hours of debate.

Under the bill, same-sex couples will be able to legally register their relationships and receive the same legal entitlements as married couples.

It is also expected to pass when the bill goes to the upper house with the support of the Greens.

Among those who spoke in support of the bill were several Labor MPs including Gerard Martin, Carmel Tebbutt and Verity Firth, as well as Independent MP Clover Moore.

Opposition leader, Liberal, Barry O’Farrell supported the bill but the current NSW Premier Kristina Keneally was absent from the debate.

Liberal MP Peter Debnam, who was in support of the register, highlighted the premier’s absence as well as her Catholic beliefs, and urged her to state her position in relation to the bill. During the debate, parliament heard concerns that the bill will undermine the institution of marriage, threaten traditional families, and have implications on state adoption laws. Speaking against the bill, Nationals Leader Andrew Stoner expressed concern in the government allowing couples who are unable to marry obtain formal recognition through the registry. He also feared that the definition of ‘de facto relationship’ will be expanded to include a new description – ‘registered relationships’.

“It is my belief that these provisions represent a significant erosion of the concept and institution of marriage in our society,” Stoner said.

The ease in which couples can register their relationships was also matter of concern.

Greg Smith, the Liberal MP for Epping, feared that the bill would pave the way for same-sex adoption.

Several MPs also raised concern at the speed in which the bill was introduced and the late hour in which it was being debated. Debnam questioned why the bill was pushed through at an unscheduled night sitting of parliament, on the same night the federal government releasesd its budget.

"Bearing that in mind, one could reach only one conclusion about this bill: the Government is trying to hide it. And that is a sad state of affairs, because the bill is very important and many people would like to hear about it," Debnam said.

Labor MP Barry Collier, the Parliamentary Secretary to the Attorney General, moved to address these concerns, saying the bill “does not seek to replace the institution of marriage” as the Marriage Act is under federal law.

Gay activists has publicly stated that although it is a step forward to equality - it is nothing more than the process of registering a pet dog with the council, and possibly another attempt at government to financially benefit from same sex couples (via taxation etc) without delivering them full equality granted to heterosexual coupled citizens.

Rallies are planned for this Saturday in major cities throughout Australia for the further push of same sex marriage rights.